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source: branches/f4grobner/mx-grobner.lisp@ 1746

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1;;; -*- Mode: Lisp -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
24;; Load this file into Maxima to bootstrap the Grobner package.
25;; NOTE: This file does use symbols defined by Maxima, so it
26;; will not work when loaded in Common Lisp.
27;;
28;; DETAILS: This file implements an interface between the Grobner
29;; basis package NGROBNER, which is a pure Common Lisp package, and
30;; Maxima. NGROBNER for efficiency uses its own representation of
31;; polynomials. Thus, it is necessary to convert Maxima representation
32;; to the internal representation and back. The facilities to do so
33;; are implemented in this file.
34;;
35;; Also, since the NGROBNER package consists of many Lisp files, it is
36;; necessary to load the files. It is possible and preferrable to use
37;; ASDF for this purpose. The default is ASDF. It is also possible to
38;; simply used LOAD and COMPILE-FILE to accomplish this task.
39;;
40;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
41
42(in-package :maxima)
43
44(macsyma-module cgb-maxima)
45
46
47(eval-when
48 #+gcl (load eval)
49 #-gcl (:load-toplevel :execute)
50 (format t "~&Loading maxima-grobner ~a ~a~%"
51 "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
52
53;;FUNCTS is loaded because it contains the definition of LCM
54($load "functs")
55#+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
56
57(use-package :ngrobner)
58
59
60;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
61;;
62;; Maxima expression ring
63;;
64;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
65;;
66;; This is how we perform operations on coefficients
67;; using Maxima functions.
68;;
69;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
70
71(defparameter +maxima-ring+
72 (make-ring
73 ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
74 :parse #'(lambda (expr)
75 (when modulus (setf expr ($rat expr)))
76 expr)
77 :unit #'(lambda () (if modulus ($rat 1) 1))
78 :zerop #'(lambda (expr)
79 ;;When is exactly a maxima expression equal to 0?
80 (cond ((numberp expr)
81 (= expr 0))
82 ((atom expr) nil)
83 (t
84 (case (caar expr)
85 (mrat (eql ($ratdisrep expr) 0))
86 (otherwise (eql ($totaldisrep expr) 0))))))
87 :add #'(lambda (x y) (m+ x y))
88 :sub #'(lambda (x y) (m- x y))
89 :uminus #'(lambda (x) (m- x))
90 :mul #'(lambda (x y) (m* x y))
91 ;;(defun coeff-div (x y) (cadr ($divide x y)))
92 :div #'(lambda (x y) (m// x y))
93 :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
94 :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
95 ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
96 :gcd #'(lambda (x y) ($gcd x y))))
97
98;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
99;;
100;; Maxima expression parsing
101;;
102;;
103;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
104;;
105;; Functions and macros dealing with internal representation
106;; structure.
107;;
108;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
109
110(defun equal-test-p (expr1 expr2)
111 (alike1 expr1 expr2))
112
113(defun coerce-maxima-list (expr)
114 "Convert a Maxima list to Lisp list."
115 (cond
116 ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
117 (t expr)))
118
119(defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
120
121;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
122;;
123;; Order utilities
124;;
125;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
126
127(defun find-ring-by-name (ring)
128 "This function returns the ring structure bases on input symbol."
129 (cond
130 ((null ring) nil)
131 ((symbolp ring)
132 (case ring
133 ((maxima-ring :maxima-ring #:maxima-ring $expression_ring #:expression_ring)
134 +maxima-ring+)
135 ((ring-of-integers :ring-of-integers #:ring-of-integers $ring_of_integers) +ring-of-integers+)
136 (otherwise
137 (mtell "~%Warning: Ring ~M not found. Using default.~%" ring))))
138 (t
139 (mtell "~%Ring specification ~M is not recognized. Using default.~%" ring)
140 nil)))
141
142(defun find-order-by-name (order)
143 "This function returns the order function bases on its name."
144 (cond
145 ((null order) nil)
146 ((symbolp order)
147 (case order
148 ((lex :lex $lex #:lex)
149 #'lex>)
150 ((grlex :grlex $grlex #:grlex)
151 #'grlex>)
152 ((grevlex :grevlex $grevlex #:grevlex)
153 #'grevlex>)
154 ((invlex :invlex $invlex #:invlex)
155 #'invlex>)
156 (otherwise
157 (mtell "~%Warning: Order ~M not found. Using default.~%" order))))
158 (t
159 (mtell "~%Order specification ~M is not recognized. Using default.~%" order)
160 nil)))
161
162(defun find-ring-and-order-by-name (&optional
163 (ring (find-ring-by-name $poly_coefficient_ring))
164 (order (find-order-by-name $poly_monomial_order))
165 (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
166 (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order))
167 &aux
168 (ring-and-order (make-ring-and-order
169 :ring ring
170 :order order
171 :primary-elimination-order primary-elimination-order
172 :secondary-elimination-order secondary-elimination-order)))
173 "Build RING-AND-ORDER structure. The defaults are determined by various Maxima-level switches,
174which are names of ring and orders."
175 ring-and-order)
176
177(defun maxima->poly (expr vars
178 &optional
179 (ring-and-order (find-ring-and-order-by-name))
180 &aux
181 (vars (coerce-maxima-list vars))
182 (ring (ro-ring ring-and-order)))
183 "Convert a maxima polynomial expression EXPR in variables VARS to
184internal form. This works by first converting the expression to Lisp,
185and then evaluating the expression using polynomial arithmetic
186implemented by the POLYNOMIAL package."
187 (labels ((parse (arg) (maxima->poly arg vars ring-and-order))
188 (parse-list (args) (mapcar #'parse args)))
189 (cond
190 ((eql expr 0) (make-poly-zero))
191 ((member expr vars :test #'equal-test-p)
192 (let ((pos (position expr vars :test #'equal-test-p)))
193 (make-poly-variable ring (length vars) pos)))
194 ((free-of-vars expr vars)
195 ;;This means that variable-free CRE and Poisson forms will be converted
196 ;;to coefficients intact
197 (coerce-coeff ring expr vars))
198 (t
199 (case (caar expr)
200 (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
201 (mminus (poly-uminus ring (parse (cadr expr))))
202 (mtimes
203 (if (endp (cddr expr)) ;unary
204 (parse (cdr expr))
205 (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
206 (mexpt
207 (cond
208 ((member (cadr expr) vars :test #'equal-test-p)
209 ;;Special handling of (expt var pow)
210 (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
211 (make-poly-variable ring (length vars) pos (caddr expr))))
212 ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
213 ;; Negative power means division in coefficient ring
214 ;; Non-integer power means non-polynomial coefficient
215 (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
216 expr)
217 (coerce-coeff ring expr vars))
218 (t (poly-expt ring (parse (cadr expr)) (caddr expr)))))
219 (mrat (parse ($ratdisrep expr)))
220 (mpois (parse ($outofpois expr)))
221 (otherwise
222 (coerce-coeff ring expr vars)))))))
223
224(defun maxima->poly-list (expr vars
225 &optional
226 (ring-and-order (find-ring-and-order-by-name)))
227 "Convert a Maxima representation of a list of polynomials to the internal form."
228 (case (caar expr)
229 (mlist (mapcar #'(lambda (p)
230 (maxima->poly p vars ring-and-order))
231 (cdr expr)))
232 (otherwise (merror "Expression ~M is not a list of polynomials in variables ~M."
233 expr vars))))
234
235(defun maxima->poly-list-of-lists (poly-list-of-lists vars
236 &optional
237 (ring-and-order (find-ring-and-order-by-name)))
238 "Parse a Maxima representation of a list of lists of polynomials."
239 (mapcar #'(lambda (g) (maxima->poly-list g vars ring-and-order))
240 (coerce-maxima-list poly-list-of-lists)))
241
242
243
244;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
245;;
246;; Conversion from internal form to Maxima general form
247;;
248;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
249
250(defun maxima-head ()
251 (if $poly_return_term_list
252 '(mlist)
253 '(mplus)))
254
255(defun poly->maxima (poly-type object vars)
256 (case poly-type
257 (:polynomial
258 `(,(maxima-head) ,@(mapcar #'(lambda (term) (poly->maxima :term term vars)) (poly-termlist object))))
259 (:poly-list
260 `((mlist) ,@(mapcar #'(lambda (p) ($ratdisrep (poly->maxima :polynomial p vars))) object)))
261 (:term
262 `((mtimes) ,($ratdisrep (term-coeff object))
263 ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
264 vars (monom->list (term-monom object)))))
265 ;; Assumes that Lisp and Maxima logicals coincide
266 (:logical object)
267 (otherwise
268 object)))
269
270
271;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
272;;
273;; Unary and binary operation definition facility
274;;
275;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
276
277(defmacro define-unop (maxima-name fun-name
278 &optional (documentation nil documentation-supplied-p))
279 "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
280 `(defun ,maxima-name (p vars
281 &aux
282 (vars (coerce-maxima-list vars))
283 (p (parse-poly p vars)))
284 ,@(when documentation-supplied-p (list documentation))
285 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
286
287(defmacro define-binop (maxima-name fun-name
288 &optional (documentation nil documentation-supplied-p))
289 "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
290 `(defmfun ,maxima-name (p q vars
291 &aux
292 (vars (coerce-maxima-list vars))
293 (p (parse-poly p vars))
294 (q (parse-poly q vars)))
295 ,@(when documentation-supplied-p (list documentation))
296 (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
297
298
299;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
300;;
301;; Facilities for evaluating Grobner package expressions
302;; within a prepared environment
303;;
304;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
305
306#|
307(defmacro with-monomial-order ((order) &body body)
308 "Evaluate BODY with monomial order set to ORDER."
309 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
310 . ,body))
311
312(defmacro with-coefficient-ring ((ring) &body body)
313 "Evaluate BODY with coefficient ring set to RING."
314 `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
315 . ,body))
316
317(defmacro with-ring-and-order ((ring order) &body body)
318 "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
319 `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
320 (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
321 . ,body))
322
323(defmacro with-elimination-orders ((primary secondary elimination-order)
324 &body body)
325 "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
326 `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
327 (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
328 (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
329 . ,body))
330
331|#
332
333
334;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
335;;
336;; Maxima-level interface functions
337;;
338;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
339
340;; Auxillary function for removing zero polynomial
341(defun remzero (plist) (remove #'poly-zerop plist))
342
343;;Simple operators
344
345#|
346(define-binop $poly_add poly-add
347 "Adds two polynomials P and Q")
348
349(define-binop $poly_subtract poly-sub
350 "Subtracts a polynomial Q from P.")
351
352(define-binop $poly_multiply poly-mul
353 "Returns the product of polynomials P and Q.")
354
355(define-binop $poly_s_polynomial spoly
356 "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
357
358(define-unop $poly_primitive_part poly-primitive-part
359 "Returns the polynomial P divided by GCD of its coefficients.")
360
361(define-unop $poly_normalize poly-normalize
362 "Returns the polynomial P divided by the leading coefficient.")
363|#
364
365;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
366;;
367;; Macro facility for writing Maxima-level wrappers for
368;; functions operating on internal representation
369;;
370;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
371
372(defmacro with-ring-and-order (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
373 &key (polynomials nil)
374 (poly-lists nil)
375 (poly-list-lists nil)
376 (value-type nil))
377 &body
378 body
379 &aux
380 (vars (gensym))
381 (new-vars (gensym)))
382 `(let ((,vars (coerce-maxima-list ,maxima-vars))
383 ,@(when new-vars-supplied-p
384 (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
385 (poly->maxima
386 ,value-type
387 (let ((*ring-and-order* ,(find-ring-and-order-by-name)))
388 (let ,(let ((args nil))
389 (dolist (p polynomials args)
390 (setf args (cons `(,p (maxima->poly ,p ,vars *ring-and-order*)) args)))
391 (dolist (p poly-lists args)
392 (setf args (cons `(,p (maxima->poly-list ,p ,vars *ring-and-order*)) args)))
393 (dolist (p poly-list-lists args)
394 (setf args (cons `(,p (maxima->poly-list-list ,p ,vars *ring-and-order*)) args))))
395 . ,body))
396 ,(if new-vars-supplied-p
397 `(append ,vars ,new-vars)
398 vars))))
399
400
401;;Functions
402
403(defmfun $poly_expand (p vars)
404 "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
405If the representation is not compatible with a polynomial in variables VARS,
406the result is an error."
407 (with-ring-and-order ((vars) :polynomials (p) :value-type :polynomial) p))
408
409
410(defmfun $poly_expt (p n vars)
411 (with-ring-and-order ((vars) :polynomials (p) :value-type :polynomial)
412 (poly-expt *ring-and-order* p n)))
413
414#|
415
416
417(defmfun $poly_content (p vars)
418 (with-parsed-polynomials ((vars) :polynomials (p))
419 (poly-content +maxima-ring+ p)))
420
421(defmfun $poly_pseudo_divide (f fl vars
422 &aux (vars (coerce-maxima-list vars))
423 (f (parse-poly f vars))
424 (fl (parse-poly-list fl vars)))
425 (multiple-value-bind (quot rem c division-count)
426 (poly-pseudo-divide +maxima-ring+ f fl)
427 `((mlist)
428 ,(coerce-to-maxima :poly-list quot vars)
429 ,(coerce-to-maxima :polynomial rem vars)
430 ,c
431 ,division-count)))
432
433(defmfun $poly_exact_divide (f g vars)
434 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
435 (poly-exact-divide +maxima-ring+ f g)))
436
437(defmfun $poly_normal_form (f fl vars)
438 (with-parsed-polynomials ((vars) :polynomials (f)
439 :poly-lists (fl)
440 :value-type :polynomial)
441 (normal-form +maxima-ring+ f (remzero fl) nil)))
442
443(defmfun $poly_buchberger_criterion (g vars)
444 (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
445 (buchberger-criterion +maxima-ring+ g)))
446
447(defmfun $poly_buchberger (fl vars)
448 (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
449 (buchberger +maxima-ring+ (remzero fl) 0 nil)))
450
451(defmfun $poly_reduction (plist vars)
452 (with-parsed-polynomials ((vars) :poly-lists (plist)
453 :value-type :poly-list)
454 (reduction +maxima-ring+ plist)))
455
456(defmfun $poly_minimization (plist vars)
457 (with-parsed-polynomials ((vars) :poly-lists (plist)
458 :value-type :poly-list)
459 (minimization plist)))
460
461(defmfun $poly_normalize_list (plist vars)
462 (with-parsed-polynomials ((vars) :poly-lists (plist)
463 :value-type :poly-list)
464 (poly-normalize-list +maxima-ring+ plist)))
465
466(defmfun $poly_grobner (f vars)
467 (with-parsed-polynomials ((vars) :poly-lists (f)
468 :value-type :poly-list)
469 (grobner +maxima-ring+ (remzero f))))
470
471(defmfun $poly_reduced_grobner (f vars)
472 (with-parsed-polynomials ((vars) :poly-lists (f)
473 :value-type :poly-list)
474 (reduced-grobner +maxima-ring+ (remzero f))))
475
476(defmfun $poly_depends_p (p var mvars
477 &aux (vars (coerce-maxima-list mvars))
478 (pos (position var vars)))
479 (if (null pos)
480 (merror "~%Variable ~M not in the list of variables ~M." var mvars)
481 (poly-depends-p (parse-poly p vars) pos)))
482
483(defmfun $poly_elimination_ideal (flist k vars)
484 (with-parsed-polynomials ((vars) :poly-lists (flist)
485 :value-type :poly-list)
486 (elimination-ideal +maxima-ring+ flist k nil 0)))
487
488(defmfun $poly_colon_ideal (f g vars)
489 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
490 (colon-ideal +maxima-ring+ f g nil)))
491
492(defmfun $poly_ideal_intersection (f g vars)
493 (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
494 (ideal-intersection +maxima-ring+ f g nil)))
495
496(defmfun $poly_lcm (f g vars)
497 (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
498 (poly-lcm +maxima-ring+ f g)))
499
500(defmfun $poly_gcd (f g vars)
501 ($first ($divide (m* f g) ($poly_lcm f g vars))))
502
503(defmfun $poly_grobner_equal (g1 g2 vars)
504 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
505 (grobner-equal +maxima-ring+ g1 g2)))
506
507(defmfun $poly_grobner_subsetp (g1 g2 vars)
508 (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
509 (grobner-subsetp +maxima-ring+ g1 g2)))
510
511(defmfun $poly_grobner_member (p g vars)
512 (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
513 (grobner-member +maxima-ring+ p g)))
514
515(defmfun $poly_ideal_saturation1 (f p vars)
516 (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
517 :value-type :poly-list)
518 (ideal-saturation-1 +maxima-ring+ f p 0)))
519
520(defmfun $poly_saturation_extension (f plist vars new-vars)
521 (with-parsed-polynomials ((vars new-vars)
522 :poly-lists (f plist)
523 :value-type :poly-list)
524 (saturation-extension +maxima-ring+ f plist)))
525
526(defmfun $poly_polysaturation_extension (f plist vars new-vars)
527 (with-parsed-polynomials ((vars new-vars)
528 :poly-lists (f plist)
529 :value-type :poly-list)
530 (polysaturation-extension +maxima-ring+ f plist)))
531
532(defmfun $poly_ideal_polysaturation1 (f plist vars)
533 (with-parsed-polynomials ((vars) :poly-lists (f plist)
534 :value-type :poly-list)
535 (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
536
537(defmfun $poly_ideal_saturation (f g vars)
538 (with-parsed-polynomials ((vars) :poly-lists (f g)
539 :value-type :poly-list)
540 (ideal-saturation +maxima-ring+ f g 0 nil)))
541
542(defmfun $poly_ideal_polysaturation (f ideal-list vars)
543 (with-parsed-polynomials ((vars) :poly-lists (f)
544 :poly-list-lists (ideal-list)
545 :value-type :poly-list)
546 (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
547
548(defmfun $poly_lt (f vars)
549 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
550 (make-poly-from-termlist (list (poly-lt f)))))
551
552(defmfun $poly_lm (f vars)
553 (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
554 (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
555
556|#
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